New directions in algebraic statistics: Three challenges from 2023
arxiv(2024)
摘要
In the last quarter of a century, algebraic statistics has established itself
as an expanding field which uses multilinear algebra, commutative algebra,
computational algebra, geometry, and combinatorics to tackle problems in
mathematical statistics. These developments have found applications in a
growing number of areas, including biology, neuroscience, economics, and social
sciences.
Naturally, new connections continue to be made with other areas of
mathematics and statistics. This paper outlines three such connections: to
statistical models used in educational testing, to a classification problem for
a family of nonparametric regression models, and to phase transition phenomena
under uniform sampling of contingency tables. We illustrate the motivating
problems, each of which is for algebraic statistics a new direction, and
demonstrate an enhancement of related methodologies.
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